Your Nathaniel Thayer is covered by Patricia Thayer Muno in her 2000 book "Descendants of Nathaniel Thayer Immigrant to America 1660" which is volume II in her "Comprehensive Genealogy of the Thayer Family of America"
Nathaniel Thayer was baptized 10 May 1640 in Thornbury, Gloucester, England.He was the son of William Thayer and Mary Kellaway.He died c. 1725 in Taunton, Bristol, MA. He married Abigail Harvey c. 1660.She was born 25 Apr 1640 in Boston, Suffolk, MA the daughter of William Harvey & Joan Hucker.She died 20 Aug 1691 in Taunton.
Their daughter Deborah was born c. 1682 in Taunton.She married James Codding, b. 1680 in Dighton, Bristol, MA
If you want any more info let me know. Calvin Thayer Wright CalvinTW@aol.com